• Structural Engineering and Mechanics
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• v.62 no.1
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• pp.85-95
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• 2017

This paper presents an explicit analytical iteration method for form-finding analysis of suspension bridges. By extending the conventional analytical form-finding method predicated on the elastic catenary theory, two nonlinear governing equations are derived for calculating the accurate unstrained lengths of the entire cable systems both the main cable and the hangers. And for the gradient-based iteration method, the derivation of explicit calculation for the Jacobian matrix while solving the nonlinear governing equation enhances the computational efficiency. The results from sensitivity analysis show well performance of the explicit Jacobian matrix compared with the traditional finite difference method. According to two numerical examples of long span suspension bridges studied, the proposed method is also compared with those reported approaches or the fundamental criterions in suspension bridge structural analysis, which eventually confirms the accuracy and efficiency of the proposed approach.

• Smart Structures and Systems
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• v.21 no.5
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• pp.695-703
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• 2018

Based on monitoring data collected from the Nanjing Dashengguan Bridge over the last five years, this paper systematically investigates the effects of temperature field and train loadings on the structural responses of this long-span high-speed railway bridge, and establishes the early warning thresholds for various structural responses. Then, some lessons drawn from the structural health monitoring system of this bridge are summarized. The main context includes: (1) Polynomial regression models are established for monitoring temperature effects on modal frequencies of the main girder and hangers, longitudinal displacements of the bearings, and static strains of the truss members; (2) The correlation between structural vibration accelerations and train speeds is investigated, focusing on the resonance characteristics of the bridge at the specific train speeds; (3) With regard to various static and dynamic responses of the bridge, early warning thresholds are established by using mean control chart analysis and probabilistic analysis; (4) Two lessons are drawn from the experiences in the bridge operation, which involves the lacks of the health monitoring for telescopic devices on the beam-end and bolt fractures in key members of the main truss.

• Journal of the Earthquake Engineering Society of Korea
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• v.10 no.6 s.52
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• pp.9-18
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• 2006

This paper presents schematically the monitoring system installed in Yongjong Bridge, a self-anchored suspension bridge located in the expressway linking Seoul and Incheon International Airport. Automatic measurement of instrumented civil engineering structures is now widely applied for behavior monitoring during construction in field as well as long-term monitoring for lifetime assessment of bridge structures. A representative example of results that can be acquired through structural health monitoring system is presented by means of data measured during a few years after the opening of the bridge. In order to effectively measure the tension force for hangers that have relatively short length or high tension force, a static tension measurement device has been explored. Newly equipped railway system on the existing bridge results in change of dead load, consequently dynamic characteristics have also been changed. This result can be detected by the monitoring system during and after railway construction.

• Structural Monitoring and Maintenance
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• v.3 no.4
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• pp.349-375
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• 2016

The tension of an arch bridge hanger is estimated using a number of experimentally identified modal frequencies. The hanger is connected through metallic plates to the bridge deck and arch. Two different categories of model classes are considered to simulate the vibrations of the hanger: an analytical model based on the Euler-Bernoulli beam theory, and a high-fidelity finite element (FE) model. A Bayesian parameter estimation and model selection method is used to discriminate between models, select the best model, and estimate the hanger tension and its uncertainty. It is demonstrated that the end plate connections and boundary conditions of the hanger due to the flexibility of the deck/arch significantly affect the estimate of the axial load and its uncertainty. A fixed-end high fidelity FE model of the hanger underestimates the hanger tension by more than 20 compared to a baseline FE model with flexible supports. Simplified beam models can give fairly accurate results, close to the ones obtained from the high fidelity FE model with flexible support conditions, provided that the concept of equivalent length is introduced and/or end rotational springs are included to simulate the flexibility of the hanger ends. The effect of the number of experimentally identified modal frequencies on the estimates of the hanger tension and its uncertainty is investigated.

• Structural Engineering and Mechanics
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• v.56 no.6
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• pp.939-957
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• 2015

In this paper, a new approach based on the continuum model is proposed to estimate the main cable tension force of suspension bridges from measured natural frequencies. This approach considered the vertical vibration of a main cable hinged at both towers and supported by an elastic girder and hangers along its entire length. The equation reflected the relationship between vibration frequency and horizontal tension force of a main cable was derived. To avoid to generate the additional cable tension force by sag-extensibility, the analytical solution of characteristic equation for anti-symmetrical vibration mode of the main cable was calculated. Then, the estimation of main cable tension force was carried out by anti-symmetric characteristic frequency vector. The errors of estimation due to characteristic frequency deviations were investigated through numerical analysis of the main cable of Taizhou Bridge. A field experiment was conducted to verify the proposed approach. Through measuring and analyzing the responses of a main cable of Taizhou Bridge under ambient excitation, the horizontal tension force of the main cable was identified from the first three odd frequencies. It is shown that the estimated results agree well with the designed values. The proposed approach can be used to conduct the long-term health monitoring of suspension bridges.

• Structural Engineering and Mechanics
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• v.87 no.3
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• pp.255-272
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• 2023

Spatial cable systems can provide more transverse stiffness and torsional stiffness without sacrificing the vertical bearing capacity compared with conventional vertical cable systems, which is quite lucrative for long-span earth-anchored suspension bridges' development. Higher economy highlights the importance of refined form-finding analysis. Meanwhile, the internal connection between the lateral and vertical sags has not yet been specified. Given this, an analytic algorithm of form-finding for the earth-anchored suspension bridge with spatial cables is proposed in this paper. Through the geometric compatibility condition and mechanical equilibrium condition, the expressions for cable segment, the recurrence relationship between catenary parameters and control equations of spatial cable are established. Additionally, the nonlinear general reduced gradient method is introduced into fast and high-precision numerical analysis. Furthermore, the analytic expression of the lateral and vertical sags is deduced and discussed. This is very significant for the space design above the bridge deck and the optimization of the sag-to-span ratio in the preliminary design stage of the bridge. Finally, the proposed method is verified with the aid of two examples, one being an operational self-anchored suspension bridge (with spatial cables and a 260 m main span), and the other being an earth-anchored suspension bridge under design (with spatial cables and a 500 m main span). The necessity of an iterative calculation for hanger tensions on earth-anchored suspension bridges is confirmed. It is further concluded that the main cable and their connected hangers are in very close inclined planes.

• Structural Engineering and Mechanics
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• v.90 no.4
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• pp.325-343
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• 2024

Triple-tower double-cable suspension bridges have increased confinement stiffness imposed by the main cable on the middle tower, which has bright application prospects. However, vertical bending and torsional vibrations of the double-cable and the girder are coupled in such bridges due to the hangers. In particular, the bending vibration of the towers in the longitudinal direction and torsional vibrations about the vertical axis influence the vertical bending and torsional vibrations of the stiffening girders, respectively. The conventional analytical algorithm for assessing the dynamic features of the suspension bridge is not directly applicable to this type of bridge. This study attempts to mitigate this problem by introducing an analytical algorithm for solving the triple-tower double-cable suspension bridge's natural frequencies and mode shapes. D'Alembert's principle is employed to construct the differential equations of the vertical bending and torsional vibrations of the stiffening girder continuum in each span. Vibrations of stiffening girders in each span are interrelated via the vibrations of the main cables and the bridge towers. On this basis, the natural frequencies and mode shapes are derived by separating variables. The proposed algorithm is then applied to an engineering example. The natural frequencies and mode shapes of vertical bending and torsional vibrations derived by the analytical algorithm agreed well with calculations via the finite element method. The fundamental frequency of vertical bending and first- and second-order torsion frequencies of double-cable suspension bridges are much higher than those of single-cable suspension bridges. The analytical algorithm has high computational efficiency and calculation accuracy, which can provide a reference for selecting appropriate structural parameters to meet the requirements of dynamics during the preliminary design.

• Steel and Composite Structures
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• v.47 no.1
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• pp.51-69
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• 2023

In tied-arch bridges, a properly designed connection between the arch and the deck may become crucial, since the forces in the structure may be significantly reduced. This implies substantial material savings and, consequently, cheaper constructions. The introduction of the Nielsen cable arrangement (composed of V-shaped inclined hangers) in the last century was a milestone because it was able to reduce deflections and bending moments both in the arch and in the deck. So far, the Nielsen cable arrangement has proven to be successful in traditional vertical arch bridges. However, despite its advantages, it has not been widely applied to spatial arch bridges. Thus, this article analyses the difference between the structural behavior of spatial arch bridges with Nielsen-type cable arrangements with respect to those with classical vertical hanger configurations. The main goal is to verify whether the known effectiveness of the Nielsen cable arrangement for classical arch bridges is still preserved when applied to spatial arch bridges. In order to achieve this objective, and as the first part of our study, a set of different all-steel bridges composed of vertical and inclined arches with straight decks have been compared for both cable arrangements. As a major conclusion, for planar vertical arch bridges, the Nielsen-type cable arrangement is always the most effective. In addition, it also seems that, for spatial arch bridges composed of a straight deck and an inclined arch, it still keeps most of its effectiveness as long as the arch is moderately inclined.

• Steel and Composite Structures
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• v.22 no.5
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• pp.1001-1018
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• 2016

The purpose of this paper is to compare the structural responses obtained from the stochastic analysis of a suspension bridge subjected to uniform and partially correlated seismic ground motions, using different spatial correlation functions commonly used in the earthquake engineering. The spatial correlation function employed in this study consists of a term that characterizes the loss of coherency. To account for the spatial variability of ground motions, the widely used four loss of coherency models in the literature has been taken into account in this study. Because each of these models has its own characteristics, it is intended to determine the sensitivity of a suspension bridge due to these losses of coherency models which represent the spatial variability of ground motions. Bosporus Suspension Bridge connects Europe to Asia in Istanbul is selected as a numerical example. The bridge has steel towers that are flexible, inclined hangers and a steel box-deck of 1074 m main span, with side spans of 231 and 255 m on the European and Asian sides, respectively. For the ground motion the filtered white noise model is considered and applied in the vertical direction, the intensity parameter of this model is obtained by using the S16E component of Pacoima Dam record of 1971 San Fernando earthquake. An analytically simple model called as filtered white noise ground motion model is chosen to represent the earthquake ground motion. When compared with the uniform ground motion case, the results obtained from the spatial variability models with partial correlation outline the necessity to include the spatial variability of ground motions in the stochastic dynamic analysis of suspension bridges. It is observed that while the largest response values are obtained for the model proposed by Harichandran and Vanmarcke, the model proposed by Uscinski produces the smallest responses among the considered partially correlated ground motion models. The response values obtained from the uniform ground motion case are usually smaller than those of the responses obtained from the partially correlated ground motion cases. While the response values at the flexible parts of the bridge are totally dominated by the dynamic component, the pseudo-static component also has significant contributions for the response values at the rigid parts of the bridge. The results also show the consistency of the spatial variability models, which have different characteristics, considered in this study.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.2A
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• pp.215-222
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• 2008

This paper introduces an experimental verification of a tension estimation method based on system identification approach for a double hanger system on a suspension bridge. A laboratory model of such double hanger system has been made for this study. Total nine cases of the vibration tests have been conducted with respect to three levels of applied tension and three cases of the location of clamp. For a set of the collected acceleration response data, modal analysis has been followed in order to extract the natural frequencies and mode shapes of the selected cable systems. For the extracted modal parameters, the existing tension estimation methods based on the string theory and axially loaded beam theory have been firstly applied to estimate the tensile force on the double hanger cable system. Next, the tensile force on cables has been estimated by the system identification approach. It is seen that the errors in the tension estimation using the frequency-based system identification technique are about 3% for all cases while the estimation error using the existing method is up to 53.1%.